Encoding from Softwares (Premiere Pro, DaVinci) in REALTIME?

To describe our situation: We mainly use softwares like Adobe Premiere Pro and DaVinci Resolve. For the postproduction and encoding we set up UltraStudio 4K Extreme 3.

Our goal is to play out our videos from the Softwares Adobe Premiere or DaVinci Resolve in Realtime to H.265.

Do you know any workflows, that could help us to realize this aim?

Please notice, that Premiere and DaVinci are unable to access the hardware encoding feature of the Ultrastudio 4K Extreme 3, and will instead only be able to encode video using the codecs which they have licenses for using the processing power of the computer.

—> Do you know any other hardware, that is able to realize realtime encoding and that can be used with the Software I mentioned?
—> Do you have any other approach to solving this problem?

Thanks for your help and input!

If you already have the UltraStudio, the cheapest way would probably be to use a different I/O device in Premiere/Resolve, and then capture to H.265 in Media Express.